Room P3.10, Mathematics Building

Orlando Neto, CMAF, Universidade de Lisboa
On the de Rham complex of an holonomic $\cal D$-module

An holonomic $\mathcal{D}$-module $\mathcal{M}$ is a system of differential equations on a complex manifold $X$ (module over the ring of differential equations on $X$) that equals a flat connection $(E,\nabla )$ on the complementary of an hypersurface $Y$ of $X$. If $\mathcal{M}$ verifies a reasonable condition the de Rham complex of $\mathcal{M}$ only depends on the the Rham complex of $(E,\nabla )$. We obtain in this way a dictionary between a certain class of linear representations of the fundamental group of $X\setminus Y$ and a certain class of holonomic $\mathcal{D}$-modules.